Irreversibility Without Entropy: Time as Index as an Interface to Landauer

Trilogy Overview: Time as Index and the Landauer Interface (Paper 3 of 3) This paper provides a conceptual and cross-disciplinary overview of irreversibility, independent of the standard thermodynamic narrative. By defining Time as Index and the structural residue known as Slip, it explains why temporal ordering arises from the simple constraints of finite memory and failed recurrence. It clarifies the role of Landauer’s principle as a "price tag" for physical implementation rather than the cause of irreversibility itself. Core Result: Structural irreversibility precedes thermodynamic dissipation. Time is an index before it is a cost. This version is designed for a general academic and cross-disciplinary audience, focusing on the logical interface between information and time.